Robust discrete-time linear control of heart rate during treadmill exercise

This paper investigates the ability to control the human heart rate during treadmill exercise which is an important issue in the development of rehabilitation protocols after surgery or weight loss programs and in the prevention of heart failure. In this way, a nonlinear model describing the heart rate response to treadmill exercise is used in this paper to design a PID-type controller adjusting the treadmill speed in a way that the heart rate tracks a reference input profile. The model parameters are estimated individually to best describe the person exercising. Afterwards, two extreme linear systems are defined from the nonlinear model. These extreme linear systems are then used to design a linear robust controller capable of providing an adequate closed-loop response for all the linear systems contained between the two extreme models. The so-designed controller is finally discretized by using a ZOH in order to obtain a discrete-time controller suitable to be implemented in practice. The designed control system is tested on the original nonlinear model by computer simulation to demonstrate the effectiveness of the proposed method to achieve the required objective.